Have a look into the Javadocs:
extended by java.awt.Container extended by java.awt.Panel extended by java.applet.Applet
Applet are Panels, and so you should be able to add them to a Frame. However, their initialization and invocation in a Frame (or JFrame) is different. Here is, btw. the JApplet version:
java.lang.Object extended by java.awt.Component extended by java.awt.Container extended by java.awt.Panel extended by java.applet.Applet extended by javax.swing.JApplet
If the Applet's code is yours, I would put all interesting content into a JPanel, and either use this JPanel in a JApplet, or put it into a JFrame, and use it as an application.
If it is not your (J)Applet, and you don't have the code, I would test to add them to a (J)Panel in a (J)Frame.